Socially Optimal Pollution Levels

Each fall, I start my undergraduate environmental economics class by asking students "What is the socially optimal level of pollution?"  The class consists of about 1/2 economics majors and 1/2 natural resource/ecology/treehugging (a joke!) majors.  Inevitably I get a critical mass of students that think zero pollution is optimal.  I tell them "If you learn one thing in this class, learn that zero pollution is not an option."  Well, I gave the final exam in that class yesterday and asked "What is the socially optimal level of pollution? Explain."  Below are a representative sample of answers.  Was I a successful teacher this quarter?  You be the judge.

Some answers from econ majors:

• We need some kind of pollution.
• The optimal level of pollution is the maximum amount we can pollute but still maintain a sustainable environment.
• We have to pollute to live.  So we just make sure our marginal costs do not exceed our marginal benefits.
• Pollution is positive for society as a whole.

Some answers Captain Planet would like.

• If economic considerations were not taken into account, the socially optimal level of pollution would be zero.  This is because no pollution would represent no cost to society. 
• The best level of pollution is the level that existed before industry raised it.  The environment naturally pollutes the level it needs to exist.

Some answers from students paying close attention is class:

• I still like 0, but it's not practical, feasible, efficient or effective.
• No matter who receives the benefits or cost, society benefits most when the marginal benefit of pollution equals the marginal cost.

And finally, here's an answer that received full credit:

• From an economic persepctive the socially optimal level of pollution occurs when the marginal benefit of the last unit of pollution exactly equals the marginal cost of pollution.  At this level the net benefits to society are maximized.  If all of the externalities of pollution are accounted for, the resulting level of pollution will be optimal.

About 50% of the class wrote something close to that.  About 75% of the class at least said marginal benefits equal marginal cost, although in the interest of full disclosure I did tell them last week that if you are clueless on an answer, MB=MC is always a good guess. 

I'm so proud.  The brainwashing is working--cue the evil professor laugh.

Comments

[joshua corning]

"the socially optimal level of pollution occurs when the marginal benefit of the last unit of pollution exactly the marginal cost of pollution."

wait wouldn't it be better if the marginal benefit exeeded the marginal cost?

yeah i am not getting this

[joshua corning]

"Pollution is positive for society as a whole."

and a Mr Burns is born.

It is good to know at least one capitalist took your class. :)

[Tim Haab]

Nope, you want teh marginal benefit to exactly equal the marginal cost. Marginal benfits are decreasing with more pollution--the first ton of sulfur dioxide is worth a lot more to the polluter than the 100th ton. The marginal costs--marginal damages-- of pollution are increasing with more pollution. The first ton of sulfur dioxide doesn't cause much damage, but the 100th does. So as long as the marginal benefits of the next unit of pollution exceeds the marginal damage, we will gain--as a society--by polluting that next unit. When will we stop? When the next unit yields no net benefit: marginal benefit equals marginal cost.

[Tim Haab]

Of course we could always work it backwards too. When should we clean up the next unit of pollution? When the marginal damages exceed the marginal benefits of that unit. So when do we stop cleaning up? When the marginal damages exactly equal the marginal benefits. Same result.

[joshua corning]

"The first ton of sulfur dioxide doesn't cause much damage, but the 100th does."

I understand now. For your teaching referance it was the sentance above that pierced its way through my thick skull.

Thanks

[tomslee]

Let me just play devil's advocate here, to search out a few of the reasons why people may be resisting MB=MC.

Are there situations where we reject MB=MC with good reason? Yes there are. Here are two:

1. What is the optimal number of prisoners (or other involuntary subjects) who should die in the pursuit of more effective medicinal treatment of potentially fatal diseases?

2. What is the optimal number of animals that we should kill in the pursuit of better hair conditioning products?

(1) says that when rights come into play, we no longer adopt the MB=MC utilitarian approach, and in fact say that the answer is zero. Can we think that this might apply to the issue of pollution? Perhaps we can, especially in the cases where those who suffer from the pollution are different from those who benefit from the production that it is a side effect of.

(2) says that the cost and benefit in MC and MB begs the question "whose cost" and "whose benefit"? If animals are included, then the balance comes at a very different point to when animals are excluded. And when it comes to the environment, there is a question of how far out from "us" do we extend the boundary of this inclusion. Do we include the fish in the lake in our cost and benefit, and if so how?

You can argue that these problems become simply a matter of evaluating MB and MC so that we can balance them (and I think that is the standard economic approach) but at some point I do think that the vagaries of that evaluation are so huge that "MB=MC" becomes meaningless.

[John Lopresti]

One senses that to teach an asymptote is to postulate its coordinates in n-dimensions. Proceeding thru the calculus of dynamic systems one could suggest ranges: If the teenager in the house plays the music system very loud the parent decides on a complex equation of permissible variables in the soundscape and the periodicity of quiet moments, aligning the quiet times with appropriate 6-1/2 hours of rest ordinary mortals require; yielding a negative coefficient for allowable noise pollution whenever the parent is irrascible, or even when the teens ascertain an approaching measure of parental opprobrium.
Pollution is relative to medium; some media are infinitely intermiscible. And contemplatively metaphorized some Platonian geometries are exquisite in the abstract from every distance. The teacher walks off to the side a slight amount. Student senses there is a rhythm as well as an asymptote.
The appropriate amount of gasoline spillage at the pump = 0? or =<0? i.e., how is it possible to spill less than zero?
Take global warming: how is it possible to cease manufacture of aerosols so the ozone hole disappears. Here we embark on colloidal chemistry and perhaps contemplate equilibrated systems. Some creative thinker might suggest counterpollutants to adsorb like the therapeutic charcoal, a medicine to heal nature of pollutants.
Alongside, a psychologist glances and remarks as if stating some abstract thesis, counseling that in our civil matrix teens are going to traverse phases, the loud boom-box, the ipod. So there are defined sets in which pollution is knowable. A poet clears the mind, energizes based on some shared multiplication factor by which the net product is more like a quantum shift than an arithmetic increment.
Your question is artful. And you seek a simple answer. Defining the detriment which is pollution in a timed test final exam is the question which I shall leave to last before I answer.
Quite the pedagogic success: to define that which exists only because its matrix must be generated a priori.
Think now, students: what is important to us.
Do we yet know how warm a 10 degree rise in temperature on the planet would be; and how much dedication it would take Very Soon Now to forestall and reverse the upslope acceleration adumbrating the global warming effect.

[Liam]

Presumably the best answer would say MC=MB OR polution=0, no? Because MC=MB assumes an interior solution, but in some cases this might not exist - it may be that any pollution will produce such large costs (perhaps it will start off a negative feedback chain reaction) that there is no point where MC=MB. Indeed, this is presumably the case with all those pollutants that have been banned completely.

[Tim Haab]

A bunch of reactions:

Liam: Good point. This is an undergraduate class with almost no background in econ required. I struggle enough to make the MB=MC point. It would be tough to go beyond that to explain corner solutions. Althought you did a nice job and I might try to do it next time.

John Lopresti:

Wow!

Tom asks:

1. What is the optimal number of prisoners (or other involuntary subjects) who should die in the pursuit of more effective medicinal treatment of potentially fatal diseases?

The point of the economic solution is to take the 'subjects' from being involuntary to being voluntary. When polluters have the implicit right to pollute, pollution victims are involuntarily exposed to costs. If we make the right explicit, or assign the right to be pollution-free to the victim then there is the opportunity for the 'victim' to choose the level of exposure. Your argument seems to be that the victim would always choose zero exposure. I would argue differently. Why do workers choose to work in dangerous occupations? Because they are compensated for the risk. People volunteer to put themselves at risk all the time if they perceive the benefits to outweight the costs. No, prisoners should not be forced to participate in involuntary medical trials. But for the right compensation, I'm sure that significantly more than zero would volunteer.

2. What is the optimal number of animals that we should kill in the pursuit of better hair conditioning products?

This one's tougher. I'm sure there are a significant number of people out there that would say 'zero.' But I'm also sure there are a significant number that are not opposed to animal testing of products. In an attempt to avoid value judgements, economists ignore them. Unpalatable? Probably, but the economic model is essentially anthropocentric and that involves a significant value judgement in itself.

[Dano]

Well, that's great I guess, Tim. You neglected scale, however and the effects to future generations when considering full credit, IMHO.

So I guess it's weighted more toward econ, which would make the class economic ecology, rather than ecological economics.

Best,

D

[Tim Haab]

Dano,

We spend a great deal of time talking about discounting and intergenerational issues when deriving the MB=MC rule. You're probably right though, the technically correct rule is PVMB=PVMC. I'm just happy they realize there are trade-offs.

And, 'environmental' is the adjective, 'economics' is the subject.

[tomslee]

Good response to my comment. Thanks.

[Dano]

I'm slightly concerned, Tim, about the result - I'm glad they recognize tradeoffs too.

Maybe I'm concerned I didn't see I=PAT in there anywhere [but PVMB=PVMC is a good start].

Scale is always important in ecology and I=PAT helps bound the time zero and the 'A' frames externalities and tradeoffs.

Plus the 'A' and 'T' helps us recognize that economics is a nested set of stuff within a larger ecology (and economics is dependent upon ecology) but ecology is not dependent upon economics [but it is affected by the scale of human economics].

Best,

D

[Tim Haab]

Dano,

In this admittedly simple setting I would argue that MC does incorporate scale. Perhaps a better way to express would be as marginal damages rather than marginal costs. The damage function would be a function of your I. The underlying economic models incorporate P, A and T. P through the number of affecting and affected agents in the system, A through the budget/wealth and cost functions and T through the assumed production technologies.

As for the ecology/economy relationship I view it as much more of a feedback system than a simple encompassing of the economy by the ecology. Economy impacts the ecology as much as the ecology impacts the economy. In other words, humans are a part of an ecological system.

At the risk of blatant self-promotion, here are abstracts from a couple of projects that I'm involved in to look at just such issues:

http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0524924

https://www.fastlane.nsf.gov/servlet/showaward?award=0410336

[Dano]

Well, I'm quite sure Tim that I'm guilty of oversimpifying, and there are certainly feedback loops.

Perhaps I should have highlighted 'dependent' and 'independent', with 'independent' being the ecosystem absent scalar considerations; I'm a Pimintel/Wackernagel/Vitousek/Costanza/Daily-type in this regard from the ecol end and a M'Gonigle/Daly-type (esp. Ecol Econ 28: 11-26) from your end. And the scale I used gets at your second para., prompting me to believe we are on the same page, but I'm looking and talking in one direction and your head is turned the other direction, probably suppressing a yawn. :o)

And self-promotion for doing good work is not bad, in my book.

BTW my old grad advisor is heavily involved in this NSF Biocomplexity work, modeling landcover change & these two abstracts are the language I spoke/thunk while at school [no one would listen to me now, on the ground, if I spoke like this which is probably why I go to Seattle a lot].

Best,

D

[Dano]

Fergot - I would have went for that sustainability minor in the BE/MUSES grant, Tim, had it been available...good stuff.

D

[John Champagne]

The optimum level of pollution in a democratic society is that level at which the number of people who think the level is too high is about equal to the number of people who think we are too strict against industry, and the number of people who think we have struck about the right balance between the competing interests is as large as possible.

A fee can be attached to the putting of pollution and the fee adjusted to bring the actual level of pollution into line with the expressed will of the people.

The fee proceeds can be disbursed to all people equally, if we all own the air and water. These proceeds would reflect the economic value of the air and water as waste removal systems for industry.

http://user.intersatx.net/jc/

[joshua corning]

"The optimum level of pollution in a democratic society is that level at which the number of people who think the level is too high is about equal to the number of people who think we are too strict against industry, and the number of people who think we have struck about the right balance between the competing interests is as large as possible."

I find this interesting becouse at least it admits that it is impossible in the real world to calculate MC. Instead it assumes that the larger the group of interested and equal parties the closer to MC thier consesus will be...there is a book I bought called "The wisdom of crowds" by James Surowiecki that touches on this. I havn't read it yet but it but I did see the guy who wrote it on c-span book TV.

One thing he did touch upon is that the average guesses of a group are often more acurate then expert opinion. and the larger the group the more acurate thier average becomes. Of course this assumes the the individuals in the group are somewhat informed.

[wiwa]

Isn't the optimal level of pollution 42?

All kidding aside though, I think a few people have touched on an interesting point. In terms of economic analysis, it's almost trivial to say MB=MC. The really hard part is quantifying the costs and benefits--and doing so in an equitable and democratic way--so that the optimal balance can be reached (or at least identified).

[Edward Bellamy]

I know this was a while ago, but... I hope somebody remembers to mention that the "optimum" MC=MB can never be achieved because the marginal valuations of losers in the optimum can never be fully accounted for due to uncertainty of the future and affect to future generations.

BTW - loved John Lopresti's comments; lots of long words, but spells "through" as "thru"!